Based on two inversion formulas for enumerating words in the free mono
id by adjacencies, we present a new approach to a class of permutation
problems having Eulerian-type generating functions. We also show that
a specialization of one of the inversion formulas gives Diekert's lif
ting to the free monoid of an inversion theorem due to Cartier and Foa
ta. (C) 1995 Academic Press, Inc.